Feature Clustering for Accelerating Parallel Coordinate Descent

Large-scale 1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, includingclassification and regression problems. High-performance algorithms andimplementations are critical to efficiently solving these problems. Building upon previous work on coordinate descent algorithms for 1-regularized problems, we introduce a novel family of algorithms called block-greedy coordinate descentthat includes, as special cases, several existing algorithms such as SCD, Greedy CD, Shotgun, and Thread-Greedy. We give a unified convergence analysis for the family of block-greedy algorithms. The analysis suggests that block-greedy coordinate descent can better exploit parallelism if features are clustered sothat the maximum inner product between features in different blocks is small. Our theoretical convergence analysis is supported with experimental results usingdata from diverse real-world applications. We hope that algorithmic approaches and convergence analysis we provide will not only advance the field, but will also encourage researchers to systematically explore the design space of algorithms for solving large-scale 1-regularization problems.